Pardon me, but your photos or terminology are backwards, or I'm confused. Your photo labelled "non drive side" sure looks like the drive side. I see chain stays and kickstand to the left or rear, and down tube to the front or right. The gears traditionally go on this side. And that's a photo of a traditional fixed cup which goes on the drive side.

The upper photo shows a traditional adjustable cup, without a lock ring or space for one. I wonder about that. You may want to measure the BB shell width in mm. It may be an oversized 73 mm shell, and you may need a new cartridge bottom bracket to fit it. A spindle may not work.